Q: Find the first derivative of g(x) = - 5 In(x)cos(r"). g'(x) =
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Q: Find the first derivative of 2cos(2 + x³). a. -6x² sin(2 + x³) b. -x² (sin 2 + x³) c. -6x² (cos…
A: daf(x)dx=adf(x)dx ; where , 'a' is constant. dcos (ax)dx =-a.sin(ax) dxndx=n.xn-1 .
Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…
A: A linear differential operator g D is called annihilates the functions fx if and only if…
Q: find (y') by Implicit differentiation e(2x+3y) = x² – In(xy³) 1 Add file
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Q: What is the critical point of the function f (x) = cos x?
A: what is the critical point of f(x)=cos(x)? for critical point, f'(x)=0
Q: Find y" by implicit differentiation. x² + 4y² = 4
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Q: Find the derivative of: 9e 7sin ( 3x*) Use e^x for e". -
A: We use chain rule to find the derivative.
Q: Find the second derivative of the following a .) 2x^3- 1/2x b.) Cos(x^2)
A: The given functions are a) 2x3 - 1/(2x) b) cos(x2)
Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORN 3x-4 1. y = Arctan 2. y = 2 Arccos (1…
A: y=Arctan3x-44
Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -
A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2
Q: f(x) = ln(cos3(2x+1)5) f'(x) = ?
A: Given that f(x) = ln(cos3(2x+1)5)
Q: use the Chain Rule to find the derivative. y = cos3(e4θ )
A: Given: The function given is y=cos3(e4θ) To determine: The derivative of the function y=cos3(e4θ)…
Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…
A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…
Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx
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Q: Find the family of antiderivatives of f(x) = sin 3x.
A: Given that f(x)=sin3x ...(1)
Q: Find by implicit differentiation. dx 1. x3 - xy + y2 = 7
A: topic - implicit derivative note - As per bartleby guidelines, we are supposed to answer only first…
Q: Use the Chain Rule to find the derivative. y = cos3(e4θ )
A: We have given y=cos3e4θ Then, dydθ=dcos3e4θdθ=3cos2e4θ-sine4θ4e4θ=-12e4θsine4θcos2e4θ
Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…
A: Solve by derivative
Q: d Verify tanh - = X 1- x2 dx
A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…
Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…
A: The annihilator of a function is a differential operator which, when operated on it, obliterates it.…
Q: Find the derivative of each function h(x) = 2x³ In x h(x) = 6e*(1 –- 5x) g(x) = 3 sin x cos x + 2x…
A: Given, The functions hx = 2x3 lnx hx = 6ex1-5x gx = 3sinx cosx +2x We have to find the…
Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…
A: The detailed solution is given below Thank you
Q: Find constants c1 and c2 such that F (x) = c1 sin 3x + c2x cos 3x is anantiderivative of f(x) = 2x…
A: Given: Fx=C1sin3x+C2cos3x and the antiderivative of F(x) is fx=2x sin3x To find the constants C1 and…
Q: 1. x² - 2xy + y² − 6x + 2 = 0
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Q: Differentiate the function: k(x) = 4 ln (x) + 2 cos x + x^2 k'(x) =
A: k(x)=4ln(x)+2cosx+x2Differentiate with respect to xk'(x)=(4×1x)+2-sinx+2xk'(x)=4x-2sinx+2x
Q: Shows the derivative function of: u³ + 2u, where u = x² + 3
A: Let's find.
Q: Let y = x(ln x)² – 2x In x. Find the value of X for which the second derivative, y" (x), equals…
A: Solve the following
Q: Find y" by implicit differentiation x2 5y2 5 + = 2 X у"-
A: Take d/dx on both sides and distribute it on the left side. Derivative of constant =0
Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).
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Q: Assuming that the derivative of arcsin(x) is indeed 1/√1 − x2, supply the justification that allows…
A: Recall the power series expansion for 1/√(1 − x2) The same can be written as: 1/√(1 − x2) = c0 +…
Q: Compute the second derivative of sin(g(x)) at x = 2, assuming that g(2) = 4, 8'(2) = 5, and g"(2) =…
A: Given: The function singx with g2=π4, g'2=5, and g''2=3, To find: The second derivative of given…
Q: Find the derivative of f(x) and solve for x sinx a. f(x) X = 6. b. f(x) e* sinx X = 0 COSX c. f(x) X…
A: Given: (1) f(x) = sin x / x at x = π/6 (2). f(x) = ex sinx at x= 0 (3). f(x) = cos x / ex at…
Q: Let f (x) = sin(4.x). Find the twenty-second derivative of f (x). D22 (f (x)) = O 42² cos(4æ) - 422…
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Q: (A) Find the first derivative of the following function: 1+ cos2x f(x) = %3D 1- cos2x |
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Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…
A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…
Q: The derivative of y = sin(e2x) is: 1. e2xcos(e2x) 2. 2cos(e2x) 3. 2e2xcos(e2x) 4. 2xcos(e2x)
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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…
A: See the detailed solution below.
Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =
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Q: Find the indicated derivative. dz x2 for z = x2 - dx 1- x - 5x2
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Q: (a) By using the chain rule and the derivative (1, if x>0 4 (1xl) ={-1, if x<0 %3D find (lx-x) vxE…
A: Use the chain rule to differentiate the above given function and than use the given derivative of…
Q: (a) Find the first derivative of the function y= la) with respect to x by using the chain rule.
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Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1
A: topic - derivative and limits
Q: Evaluate the 3rd derivative of M with respect to (x) M= x6 y3 Cos (x6 y3) if x =6 and y= 3
A: The function is M=x6y3cosx6y3. Using implicit differentiation, find dydx.…
Q: Use the chain rule to find the derivative of: cos(7 + 8x)
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Q: Compute the derivative of x(x + 2) (2x + 1)(3x + 2) y = (a) directly using the Chain and Product…
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Q: Find the derivative of y with respect to x for y = (- 7x2 – 5x + 5) (sin x + 11x) 1x + ..... The…
A: Given:- y = (-7x2-5x+5) (sin(x) +11x) To find:- Derivative of y
Q: Find the derivative of f(x) = 3r sin(-)(x) – In(r² – 1) + 8² – 5 cosh(x)
A: Find the derivative of function
Q: Find the critical numbers of the function g(x)=8x+sin8x
A: Given data: The expression for the given function is g(x)=8x+sin8x. The differentiation of the given…
Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…
A:
Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…
A: The given function = 10x+ 9x2-sin6x
Calculate h(x) if f(x) = x+3 and g(x) = sin(3x). Let h(x) = g(f(x)). What is h-1(x)?
What is [h-1(x)]'?
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- Determine whether each of the following statements is true or false, and explain why. The chain rule is used to take the derivative of a product of functions.Find f'(x) and simplify. X X - 19 f(x) = Which of the following shows the correct application of the quotient rule? O A. O B. O C. O D. f'(x) = (x)(1)-(x-19) (1) [x - 191² (x-19)(1)-(x)(1) [x-19]² (x)(1)(x-19) (1) [x]² (x-19)(1)-(x)(1) [x]²Find f'(x) and simplify. f(x)= x x+2 Which of the following shows the correct application of the quotient rule? (x)(1)-(x+2)(1) ○ A. [x]² (x)(1)-(x+2)(1) ○ B. [x+2]² (x+2)(1)-(x)(1) C. [x+2]² (x+2)(1)-(x)(1) ○ D. [x]² f'(x) = ☐
- Consider the function. g(x) = 2x* – 5x³ + 15x – 3 Find g'(x). g'(x) = Find 9"(x). g"(x) = Find g"(1) and 9ʻA g"(1) o(금)- Determine whether the function g(x) is concave up or concave down at the indicated points. (a) x = 1 concave up concave down (b) concave up concave down O OFind f(x) if F(x) = (1-ex)U(x-c).Differentiate the functions. a) f(x) = 2 – 5x +?x5 4 b) f(x) = e* + sinx c) f(x) = d) f(x) = (1 – 3x²) · e*
- The function f(x) = –3Vx+ 2 – 6 x > -2 | - has an inversef-'(x) defined on the domain x < -6. Find the inverse.Let h(x) = f(x) – g(x). If f(x) = 9x² and g(x) = 8x, what is h' (-5)? Do not include "h' (-5) =" in your answer. For example, if you found h' (-5) = 7, you would enter 7.find the first and second derivatives of the function f(x) = (x2 + 4)5